Question

Q19. By which smallest number must 5400
be multiplied to make it a perfect cube?​

Answer 1

Answer:

Smallest number that should be multiplied with 5400 to obtain a perfect cube is 5

Step-by-step explanation:

By prime factorisation of 5400, We get

5400 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5

When we group the factors by 3, We get

5400 = 2³ × 3³ × 5²

Clearly the last group has only 2 similar factors. And the missing one is an extra 5, so that the group of 3 is complete.

So the smallest number that should be multiplied with 5400 to obtain a perfect cube = 5.

5 × 5400 = 27000

$\sqrt[3]{27000} = 30$